The Relationships Among Wind, Horizontal Pressure Gradient, and Turbulent Momentum Transport During CASES-99

NOVEMBER 2013 S U N E T A L . 3397

The Relationships among Wind, Horizontal Pressure Gradient, and Turbulent Momentum Transport during CASES-99

JIELUN SUN AND DONALD H. LENSCHOW National Center for Atmospheric Research, Boulder, Colorado

LARRY MAHRT Oregon State University, Corvallis, Oregon

CARMEN NAPPO CJN Research Meteorology, Knoxville, Tennessee

(Manuscript received 20 August 2012, in ﬁnal form 21 May 2013)

ABSTRACT

Relationships among the horizontal pressure gradient, the Coriolis force, and the vertical momentum transport by turbulent fluxes are investigated using data collected from the 1999 Cooperative Atmosphere– Surface Exchange Study (CASES-99). Wind toward higher pressure (WTHP) adjacent to the ground oc- 2 curred about 50% of the time. For wind speed at 5 m above the ground stronger than 5 m s 1, WTHP occurred about 20% of the time. Focusing on these moderate to strong wind cases only, relationships among horizontal pressure gradients, Coriolis force, and vertical turbulent transport in the momentum balance are investigated. The magnitude of the downward turbulent momentum flux consistently increases with height under moderate to strong winds, which results in the vertical convergence of the momentum flux and thus provides a momentum source and allows WTHP. In the along-wind direction, the horizontal pressure gradient is observed to be well correlated with the quadratic wind speed, which is demonstrated to be an approximate balance between the horizontal pressure gradient and the vertical convergence of the turbulent momentum flux. That is, antitriptic balance occurs in the along-wind direction when the wind is toward higher pressure. In the crosswind direction, the pressure gradient varies approximately linearly with wind speed and opposes the Coriolis force, suggesting the importance of the Coriolis force and approximate geotriptic balance of the airflow. A simple one-dimensional planetary boundary layer eddy diffusivity model demonstrates the possibility of wind directed toward higher pressure for a baroclinic boundary layer and the contribution of the vertical turbulent momentum flux to this phenomenon.

1. Introduction require estimating the effects of dynamic pressure fluctuations, the angle-of-attack sensitivity of pressure probes The horizontal pressure gradient is commonly thought (Wilczak and Bedard 2004), and the sensitivity of micro- to drive the atmospheric circulation. Its magnitude is barograph output to temperature variations (Cuxart et al. typically about four orders of magnitude smaller than the 2002). Various probes have been developed to minimize vertical pressure gradient at the ground, which makes it effects of dynamic pressure fluctuations (Nishiyama and difficult to measure on small scales. Small static pressure Bedard 1991; Akyuz€ et al. 1991). perturbations can result from the effects of turbulence, Observational studies of horizontal pressure gradients flow distortion induced by nearby structures, or the pres- have concentrated on mesolows and mesohighs (e.g., sure probes themselves. Accurate pressure measurements Vescio and Johnson 1992; Johnson 2001; Adams-Selin and Johnson 2010). Fujita (1963) examined mesoscale Corresponding author address: Jielun Sun, National Center for pressure disturbances by converting time variation to Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. spatial variation when considering mesoscale system E-mail: [email protected] development in a moving synoptic environment. This

DOI: 10.1175/JAS-D-12-0233.1

Ó 2013 American Meteorological Society 3398 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70 technique has been applied to various studies of surface documentation in the literature for antitriptic balance pressure patterns in relation to mesoscale convective occurring on scales smaller than O(102 km). systems (e.g., Vescio and Johnson 1992; Adams-Selin Often, the vertical momentum transfer by the turbu- and Johnson 2010). LeMone et al. (1988) investigated the lent flux in the momentum balance is simply called the mesoscale horizontal pressure gradient under developing surface friction, especially in simple numerical models clouds using the Fujita method for aircraft and ground where this term is approximately estimated as the dif- observations. Parish et al. (2007) also estimated meso- ference between the surface drag and the near-zero tur- scale horizontal pressure gradients from aircraft static bulent momentum flux at the planetary boundary layer pressure and global positioning system measurements. (PBL) top (Bernhardt 1983; Haltiner and Williams 1990). In addition to the familiar geostrophic balance, the Under this assumption, the airflow has to be down the role of horizontal pressure gradients in the momentum pressure gradient. balance has also been considered for antitriptic and The unique observational dataset collected from the geotriptic balances. Antitriptic balance in the momentum 1999 Cooperative Atmosphere–Surface Exchange Study equation was first defined by Jeffreys (1922) as a station- (CASES-99) (Poulos et al. 2002) provides an opportunity ary atmospheric flow in a spatially varying pressure field to investigate relations among the horizontal pressure where the horizontal pressure gradient balances the gradient, wind, and vertical turbulent momentum trans- vertical turbulent momentum transport, which he called port in the momentum balance on a horizontal scale of the internal friction term. He also suggested that anti- less than 1 km. However, because of observational un- triptic flow only occurs for spatial scales of disturbances certainties discussed in section 2, we are not in a position smaller than O(102 km), for which the Coriolis force can to examine how well the momentum balances in general. be neglected. Based on the assumption of constant eddy Yet, we are able to investigate the role of the horizontal viscosity, he further suggested that the antitriptic wind is pressure gradient and its variation with other terms in the toward lower pressure and the land or sea breeze is an momentum balance during CASES-99. The observations example of an antitriptic flow. Johnson (1966) proposed and the methodology of estimating the horizontal pres- the term geotriptic balance by including the Coriolis force sure gradient and the turbulent flux used in this study are in addition to the horizontal pressure gradient and the described in section 2. In section 3, we investigate re- vertical turbulent momentum flux transport. We note lationships among the horizontal pressure gradient, the that inconsistent usage of antitriptic balance appears in vertical variation of the turbulent momentum flux, wind the literature. Saucier (1955) and Schaefer and Doswell speed, and the Coriolis force with a focus on wind toward (1980), for example, used the term antitriptic balance higher pressure (WTHP). We discuss the duration of for what Johnson calls geotriptic balance. Here we use the WTHP phenomenon, the observed conditions when Jeffreys’s original definition of antitriptic balance. wind is toward lower pressure (WTLP), and implications Antitriptic and geotriptic flows are often used to of this study for antitriptic and geotriptic balances in qualitatively describe mesoscale flows. Some examples section 4. Section 5 is a summary. are flow in mountainous terrain (McKendry et al. 1986; Bell and Bosart 1988; Colle and Mass 1996; Mass and Steenburgh 2000), flow in sloped environments (Parish 2. Observations and analysis methods and Waight 1987), and flow near the equator (Raymond a. Observations 1993). Bell and Bosart (1988) found that the surface synoptic winds were approximately opposite to the ver- All the instruments relevant to this study were de- tical divergence of the turbulent momentum flux, which scribed in Sun (2011) and Sun et al. (2012). We used the they calculated as the residual of the momentum balance, eight levels of three-dimensional sonic anemometer wind and concluded that the momentum flux divergence is measurements on the 60-m tower, as well as the wind, proportional to the surface drag. Similarly, Colle and pressure, and air temperature measurements at six 10-m- Mass (1996) calculated the turbulent momentum flux as high satellite towers surrounding the 60-m tower (Fig. 1). the residual of the momentum balance and also con- The lowest sonic anemometer was moved from 1.5 to cluded that the vertical divergence of the turbulent mo- 0.5 m on 20 October. The actual positions of the six 10-m mentum flux is a drag although the wind and the residual towers, which differ from the original plan described in terms are not in the opposite direction everywhere in Sun et al. (2002), are listed in Table 1, where x and y their study. Using the surface friction to represent the represent the distances from the 60-m tower in the east– vertical divergence of the momentum flux, Macklin west and north–south directions, respectively, and the et al. (1988) investigated geotriptic balance for offshore elevation of each tower is relative to sea level. The un- flows. Interestingly, we have found little observational certainty of the station elevation is discussed in section 2c. NOVEMBER 2013 S U N E T A L . 3399

TABLE 1. The locations of the six satellite towers.

Station Latitude Longitude Elevation x y No. (8) (8) (m) (m) (m) 1 37.648 93 296.735 07 435.9 52.9 103.5 2 37.647 50 296.736 47 433.6 270.5 255.7 3 37.648 95 296.737 18 431.8 2133.1 105.8 4 37.649 83 296.738 70 435.9 2267.1 203.7 5 37.645 95 296.736 44 433.4 267.9 2228.2 6 37.649 68 296.733 32 438.6 207.2 187

transducers used during CASES-99 with the reading from a pressure transducer with accuracy traceable to the NIST standard at preset pressure values ranging from 785 to 845 hPa. The bias of each pressure transducer was removed based on the calibration prior to CASES-99, which was still applicable for the 2013 calibration. We did not detect any time drift of the transducer output over the 100-h period of the calibration. Based on the calibration dataset, we estimate that the transducers were calibrated to an accuracy of about 0.01 hPa for the 30-min-averaged pressure values from CASES-99.

FIG. 1. (a) Contour map of the area centered on the CASES-99 c. Horizontal pressure differences 60-m tower. (b) The blue box in (a), which includes all the CASES-99 towers, is enlarged. The numbers and the cross in (b) mark the station To obtain horizontal pressure differences, the pres- numbers and the 60-m tower, respectively. The numbers in (a) mark sure difference due to elevation differences between the contour values of the elevation relative to the area mean. The the towers needs to be removed. Integrating the hy- horizontal spatial resolution of the dataset is 60 m. drostatic equation and applying the ideal gas law, we obtain b. Pressure measurements gdz During CASES-99, six identical pressure sensors were ln(pc/po) 52 , (1) R T deployed at 1.5 m above the ground on the six satellite d y towers. Each pressure sensor consists of a Vaisala where p is the air pressure, the superscripts c and PTB220B transducer and a round disk port with asym- o denote the corrected and observed values, g is the metric edges on two sides developed by the Earth Ob- gravity acceleration constant, dz is the vertical differ- servatory Laboratory (EOL) at the National Center for ence used in the elevation correction, Rd is the gas Atmospheric Research (NCAR). The performance of constant for dry air, Ty is the virtual temperature the pressure sensor depends on the transducer error and averaged over the layer dz, and the overbars represent the magnitude of dynamic pressure fluctuations induced 30-min averaging. by the pressure port. The design of the disk port mini- We use Ty estimated from the 2-m air temperature and mizes dynamic pressure fluctuations due to the airflow humidity measurements at each tower with the known attack angle relative to the disk, which are proportional to elevation differences between the towers to correct for wind speed squared. Based on the wind tunnel test de- c the elevation. Assuming an error dTy, its impact on p scribed by Akyuz€ et al. (1991), the dynamic pressure error introduces an error dpc. Based on (1), of the pressure port used during CASES-99 is less than 0.01 hPa if the standard deviation of the attack angle is ! gdzdT gdz less than 58, the mean attack angle is less than 28,and dpc 5 po y exp 2 . (2) 2 2 1 R Ty the wind speed is less than 10 m s for the roughness of RdTy d the CASES-99 site. These conditions were met during o CASES-99. If p 5 900 hPa, dz 5 1m, Ty 5 300 K, and dTy 5 1K, The NCAR EOL conducted a laboratory calibration the uncertainty in the corrected pressure is less than 2 in 2013 that compared the readings from seven pressure 4 3 10 4 hPa. 3400 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70

Assuming (pc 2 po)/po # O(1021), (1) can be ap- proximated as pc 2 po pc 2 po gdz ln(pc/po) 5 ln 1 1 ; ;2 . po po RdTy (3)

Based on (3), if there is no horizontal pressure gradient over the CASES-99 domain of about 500 m 3 500 m, and the air temperature and humidity are horizontally homogeneous, the measured pressure difference between the towers would be linearly proportional to the elevation difference between the towers. During a strong wind night of 17 October, Ty estimated from the measurements at 2 m was approximately the same at all the towers and within the lowest 8 m above the ground for about 2 h FIG. 2. The correlation between the elevation difference and the owing to the strong turbulent mixing close to the ground. pressure difference between each tower (towers 2–6) and tower 1 The observed approximately linear relationship between for the windy night of 17 Oct when the surface air temperature was spatially homogeneous near the ground. The black line represents the measured pressure difference and the elevation dif- the fitted linear relationship. ference between the towers in Fig. 2 suggests that the estimated elevation is within the pressure measurement s2 1 s2 1/2 s s accuracy for stations 4 and 6. For the air temperature of ( 1 2) , where 1 and 2 are the accuracies of sen- 282 K during this period, the pressure varies with height sors 1 and 2, depending on how well the fluctuations 2 by 20.12 hPa m 1. Station 2 is 0.6 m off the line, which is measured by the two sensors are correlated. If readings the largest offset among all the stations except station 3 at from the two sensors were identical for the same pressure a small-scale depression area. Using Fig. 2, we can esti- variation, the accuracy of the pressure difference would mate the elevation difference between the towers, which be perfect. If readings from two sensors were not corre- has an uncertainty of 0.08 m corresponding to the pres- lated at all, the accuracy of the pressure difference would s2 1 s2 1/2 sure uncertainty of 0.01 hPa. The absolute elevation of be ( 1 2) . Based on the NCAR EOL laboratory each station above sea level is irrelevant in the pressure test, we find that the measurements between the sensors difference calculation. Because the error introduced by are highly correlated and the accuracy of the 30-min- the temperature uncertainty is relatively small, the error averaged pressure differences remains around 0.01 hPa. involved in the elevation correction is mainly from the To calculate meaningful horizontal gradients of any elevation difference, which is systematic and does not variable, the accuracy of the measured difference is not affect relationships between the variation of the hori- the only concern. Another important issue is the relevant zontal pressure gradient and other variables. Possible separation between observations for calculating hori- systematic biases of the pressure measurements due to zontal gradients. If the separation is too large, the esti- the elevation uncertainty are further tested in section 3. mated gradient may not be relevant for the flow between Using (3), the observed pressure at tower i is corrected the measurement locations. For example, the airflow may relative to the elevation of tower j by change directions in between in response to forcing on " # scales smaller than the separation. If the separation is too g(z 2 z ) c 5 o 2 j i small, the sensitivity and accuracy of the instruments may pi pi 1 . (4) RdTyi not be good enough for estimating meaningful differences. A good example of investigating spatial variations To obtain the horizontal pressure gradient $p, we choose of variables is reported by Staebler and Fitzjarrald (2004, four satellite towers: two are closely aligned in the north– 2005), who characterized subcanopy motions within the south direction (towers 2 and 5, separated by 172.5 m) domain of their subcanopy-CO2-advection study. and two in the east–west direction (towers 4 and 6, sep- To ensure our estimated horizontal pressure gradient arated by 474.3 m). Based on Fig. 2, the elevation differ- make sense in the momentum balance, we investigate ence is less than 0.2 m between towers 2 and 5 and less how its variation is related to the other terms in the than 2.8 m between towers 4 and 6. momentum balance. The relationship between the var- The accuracy of pressure differences between two iation of the estimated horizontal pressure gradient and pressure sensors is theoretically between zero and the other terms would be significantly scattered if the NOVEMBER 2013 S U N E T A L . 3401 horizontal pressure gradient is not related to the other terms in the momentum equation on the spatial scale of the pressure sensor separation even though the pressure sensor is sensitive enough to capture variations of horizontal pressure differences. Therefore, we utilize the relationship between the horizontal pressure gradient and other variables in the momentum balance to judge the accuracy of the pressure gradient estimate to com- plement our horizontal pressure gradient estimates. The horizontal pressure gradient may also vary spa- FIG. 3. An example of the cumulative momentum flux in the tially within the observation domain. For example, the along-wind direction as a function of the integrated time scale using pressure gradients in x and y directions vary slightly de- the Haar wavelet method. The data are from 1600 to 1700 UTC pending on the stations used in estimating the horizontal 15 Oct, when wind was relatively strong and the wind direction varied little with height. pressure gradient. Both the largest horizontal pressure gradient and the strongest wind are in the north–south direction, so that the pressure gradient in the y direction (e.g., Fig. 3). Contribution from turbulence eddies with calculated from stations 2 and 5 gives the largest hori- a time scale of 1/f in Fig. 3 to the cumulative flux is zontal pressure gradient close to the 60-m tower. Choos- reflected in the change of the cumulative flux with 1/f. ing different towers other than stations 4 and 6 to estimate The characteristics of the turbulent fluxes in Fig. 3 of- ›p/›x changes the direction of the horizontal pressure ten occur when the atmosphere is near neutral—that is, gradient slightly. But it does not affect the main conclu- for strong wind (jz/Lj . 100, where L is the Obukhov sion in this paper as we mainly focus on moderate to length; Sun 2011). strong winds (i.e., the wind speed at 5 m above the ground Systematic underestimation of turbulent fluxes occurs 2 larger than 5 m s 1), for which the wind direction is well when a sonic anemometer cannot respond fast enough defined, the vertical variation of wind direction can be to capture small eddies, or the pathlength of the sonic ignored, and, as discussed later, the flux uncertainty from anemometer is too large to capture small turbulence intermittent submeso motions tends to be small. eddies. As a result, the turbulent momentum flux close to To compare the horizontal pressure gradient from the ground, where its dependence on the contribution of CASES-99 and independent pressure measurements small eddies is significant, can be underestimated. Horst about 56 km west of the CASES-99 site, we choose the and Oncley (2006) investigated the underestimation us- strongest horizontal pressure gradient day: 15 October. ing the transfer function as a function of eddy size relative The horizontal pressure gradient based on the surface to the pathlength for the sonic anemometer used dur- measurements between two stations separated by about ing CASES-99 and found that the underestimation for 20 km is on the same order of magnitude as the one from the fluctuations of the individual wind components is the CASES-99 site. In addition, the temporal variations of significant for eddy sizes smaller than the pathlength. the pressure at both sites are similar (more in section 4). Applying their transfer functions to the covariance between the vertical and along-wind components, we find d. Turbulent flux calculation that the contribution of the eddies smaller than the Vertical turbulent momentum fluxes consist of co- pathlength to the cumulative momentum flux is less than herent contributions from a range of eddy sizes. Assum- 0.4% at our lowest sonic anemometer level of 0.5 m for ing Taylor’s hypothesis, increasing the time period for moderate to strong winds. Thus, for a vertical flux differ- flux calculation would include flux contributions from ence of 10%, the flux difference error due to the pathlength large eddies and improve their sampling statistics. Be- averaging is less than 4% for the focus of this study, but cause the size of the dominant turbulent eddies increases may be significant for a very stably stratified flow. with height, the length of the data segment necessary to Turbulent fluxes are uncertain when the environment incorporate most of the turbulent flux using the eddy is unsteady. The covariance spectra of turbulent fluxes covariance method has to increase with height especially can be influenced by sporadic and seemingly random (for under near neutral and unstable conditions when large lack of understanding) submeso motions, which increase eddies contribute a significant portion of the turbulent uncertainty in turbulent flux estimates as demonstrated in flux. Steady turbulent fluxes can be precisely and objec- Vickers and Mahrt (2003, 2006), Mahrt (2009, 2010), and tively determined once the cumulative flux (i.e., fluxes Mahrt et al. (2012). This type of turbulent flux uncertainty integrated from small to large eddies) remains constant is fundamentally different from instrument errors. To with increasing eddy size or decreasing frequency remove the influence of submeso motions on turbulent 3402 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70

flux estimates, we rely on visual inspection of the co- Earth coordinates to investigate airflow in response to variance spectra. Overall, the impact of nonstationarity different environmental conditions in section 3c. How- on turbulent fluxes is significant at all of the observa- ever, for diagnostic studies with known wind directions, tion heights under weak winds. This nonstationarity is we use natural coordinates. less important for moderate to strong winds, but visible occasionally. 3. Role of the horizontal pressure gradient in the The turbulent momentum flux in this study is calcu- momentum balance lated as cumulative multiresolution covariances using the Haar wavelet (Howell and Sun 1999) for every 30-min We first investigate the characteristics of the hori- period, which is sufficient for the cumulative fluxes to zontal pressure gradient $p at 1.5 m above the ground. achieve statistically stable estimates at all eight observa- We find that the largest magnitude of $p is from south; tion heights. The resulting cumulative fluxes from the Haar that is, the strongest horizontal pressure gradient occurs wavelet are similar to those using the Fourier method when high pressure is north of the site (Fig. 4a, red dots). (Desjardins et al. 1989; Friehe et al. 1991). The cutoff time However, strong winds at 5 m do occur for both south- scale/frequency for determining the flux value from the erly and northerly flow (Fig. 4a, black dots). The most cumulative cospectra is selected manually for each 30-min intriguing result is in the directional difference between time segment to exclude the intermittent submeso flux wind and $p (Fig. 4b), where 50% of the observed wind from the turbulent flux. is toward higher pressure; that is, the directional differ- To investigate relationships among the variations of ence between $p andwindislessthan6908 (the points all the terms in the momentum balance, all the observed between the two black lines in Fig. 4b). A significant and derived variables in this study are averaged for 30 min fraction of these points is associated with large horizontal and include both daytime and nighttime data. pressure gradients (red dots in Fig. 4b). A significant fraction of these points has strong wind as well. For these e. Coordinates cases the wind direction is most accurate and varies little To ensure the quality of the measured pressure dif- with height. Lack of observations of $p between 1808 and ference, we investigate its relation with other terms in 3608 in Fig. 4a is due to the observed small ›p/›x com- the momentum balance in two coordinate systems. Since pared to ›p/›y and the predominantly negative ›p/›x the wind observations are in Earth coordinates, which is (Figs. 5a and 5b). Simulating the effect of uncertainty in a Cartesian coordinate system with the vertical direction the pressure measurement by arbitrarily adding a bias to 2 2 2 2 opposite from gravity, and two horizontal directions— ›p/›x of 3 3 10 5 hPa m 1 or ›p/›y of 3 3 10 4 hPa m 1 north–south (positive toward north) and east–west (positive would result in some cases in this direction range. How- toward east)—we calculate various terms in Earth co- ever, the shifting would not totally eliminate the WTHP ordinates first. However, there are advantages to ana- phenomenon, especially for the strong wind and large lyzing the observations in natural coordinates (Holton pressure gradient cases. 1979), which consist of along-wind, crosswind (positive The relationship between the directions of wind and direction is 908 counterclockwise from the wind direc- $p is further examined in terms of the fraction of the tion), and vertical upward axes. The flow acceleration wind direction relative to the $p direction in six wind term only appears in the along-wind direction, and the speed categories (Figs. 4c and 4d). For wind speed 2 relatively small Coriolis force with the Coriolis pa- stronger than 10 m s 1 (yellow vectors in Fig. 4d), all 24 21 rameter fc of approximately O(10 s ) only appears vectors are toward higher pressure despite the fact that in the crosswind direction. The turbulent momentum the pressure gradient acts to decelerate the flow under 2 flux is much stronger in the along-wind direction than these conditions. For wind speed less than 2 m s 1 (dark in the crosswind direction especially for strong winds. blue vectors in Fig. 4c), wind is observed in all directions Analyzing observations in natural coordinates allows relative to the $p direction with slightly higher than 50% us to distinguish different momentum balances in the in the direction opposite to $p (i.e., wind toward lower two perpendicular directions, which may have terms of pressure). very different magnitudes. To investigate vertical varia- We then examine the relationship between the mag- tions of turbulent fluxes in natural coordinates for mod- nitude of $p and the wind speed at 5 m S in both Earth erate to strong winds, the 30-min-averaged wind vectors and natural coordinate systems (Figs. 5a–d). The 5-m at all the observation levels are rotated to the wind di- level is the lowest observation level that had continuous rection at 5 m. turbulence measurements throughout the experiment. In prognostic studies, it is difficult to use natural co- Along the y direction, which has the largest $p and mean ordinates because of varying wind direction. We use wind, ›p/›y and the south wind component at 5-m y are NOVEMBER 2013 S U N E T A L . 3403

FIG. 4. (a) The relationships between the observed wind direction (WD) and wind speed at 5 m S (black), and between the direction of $p and its magnitude j$pj (red) for the entire 30-min-averaged dataset. The vertical red bars mark the directional error of $p as a function of j$pj due to inaccuracy of the pressure transducer. (b) The directional difference between WD and $p as a function of S, where the red dots denote j$pj . 2 3 1024 hPa m21, the two horizontal black lines denote the directional boundaries for WTHP, and the black error bar marks the uncertainty of the $p direction at j$pj 5 2 3 1024 hPa m21. (c),(d) The fractional distribution of WD relative to the $p direction for 2 six wind speed (m s 1) categories. The length of each colored vector represents the fraction of the observations in that wind speed category. For example, all vectors of S . 10 m s21 (yellow) are toward higher pressure, and the sum of their lengths equals one. For the weak wind of S , 2ms21, the blue vectors are in all directions relative to the $p direction, but the fraction in each direction is relatively small. well correlated across the observed range of y (the green To further investigate whether WTHP is realistic, we curve in Fig. 5a); furthermore, ›p/›y and the north wind examine the relationships among various terms in the component are relatively well correlated as well (the momentum balance. The momentum balance in Earth magenta curve in Fig. 5a). In natural coordinates, the coordinates can be expressed as › › along-wind pressure gradient p/ s and the crosswind 0 0 › › du 1 ›p ›w u pressure gradient p/ n are well correlated with S 2 f y 52 2 c r › › , (5) (Figs. 5c and 5d) although the correlation differs for dt x z southerly and northerly winds (more discussion in section › › 0 0 3b). The large range of the p/ y variation is reﬂected in dy 1 ›p ›w y › › 1 f u 52 2 , (6) p/ s as the strong wind cases are dominated by a strong dt c r ›y ›z southerly wind component. The wind speed is never zero when j$pj is small during CASES-99. WTHP (positive where u, y, and w are wind components in x, y, and z ›p/›s) occurs much more often under moderate to strong directions; r is the air density; and the primes represent winds than WTLP (negative ›p/›s)—that is, 22% versus their perturbations relative to their 30-min means. The 6% for S . 5ms21 (Figs. 5e and 5f). ﬁrst and second terms on the left-hand side of both (5) 3404 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70

FIG. 5. The relationships (a) between ›p/›y and y at 5 m, (b) between ›p/›x and u at 5 m, (c) between ›p/›s and S at 5 m, and (d) between ›p/›n and S. (e),(f) The fractional distributions of ›p/›s and ›p/›n in two wind speed categories, where positive ›p/›s corresponds to WTHP. In (a)–(c), the black and yellow colors represent the cases for y . 0 and for y , 0, respectively. In (a), the green and magenta curves represent the fitted relationship between ›p/›y and y2 for y . 5ms21 and for y , 0, respectively. Similar to (a), the green and solid magenta curves in (c) represent the fitted 2 relationship between ›p/›s and S for y . 5ms21 and for y , 0, respectively. The dashed magenta curve in (c) is the magenta curve flipped at ›p/›s 5 0 for comparison with the green one. and (6) are the flow acceleration and the Coriolis force, terms, such as ›u0u0/›x, ›u0y0/›x, ›yy0/›y,and›u0y0/›y,are respectively, and the last term on the right-hand side of assumed to be negligible, which should be valid at least both equations is the vertical turbulent momentum undermoderatetostrongwinds. transport. In the above momentum equations, the viscous In comparison, the momentum balance in natural stress associated with molecular motions is neglected coordinates is expressed as (Schlichting and Gersten (Garratt 1992). The horizontal momentum flux transport 2000) NOVEMBER 2013 S U N E T A L . 3405

dS 1 ›p ›w0y0 52 2 s , (7) dt r ›s ›z

2 S 1 ›p ›w0y0 1 f S 52 2 n , (8) R c r ›n ›z where R is the curvature radius of the air parcel trajectory, and the subscripts s and n represent along- and crosswind components—that is, s and n (908 anticlock- wise from s), respectively. Although the mean crosswind is zero in natural coordinates, the crosswind perturbation can contribute to the crosswind momentum flux. The concept of antitriptic and geotriptic balances men- tioned in the introduction can be clearly identified in natural coordinates when the acceleration is zero. The momentum balance is antitriptic in the along-wind direction and geotriptic in the crosswind direction under equilibrium conditions. Overall, airflow cannot be in antitriptic balance unless the Coriolis force can be neglected in comparison with the curvature term in the crosswind direction; that is, a Rossby number, defined by Ro 5 fc/(RS), is small. The horizontal wind is traditionally thought to be forced by the horizontal pressure gradient while the contribution of the turbulent flux to the momentum balance is thought to be a drag, friction, internal friction, or frictional force in the literature (e.g., Jeffreys 1922; Johnson 1966). Because of zero wind speed at the ground, FIG. 6. Geotriptic balance among the horizontal pressure the turbulent momentum flux itself is downward near the 52$ 52 0y0 , gradient force (Fp p),theCoriolisforce(Fc fcVn), and ground (i.e., w s 0), and the turbulent momentum flux 52› 0y 0 › the turbulence transport of momentum (FT w s/ zs)for is commonly called turbulent stress. However the con- › 0y 0 › . › 0y 0 › , › 0y 0 › (a) w s/ z 0and(b) w s/ z 0 if we assume w n/ z is tribution of the turbulence transport to the momentum negligible. The vertical lines represent pressure contours. balance in (7) is not the turbulent momentum flux itself, but the vertical divergence of the turbulent momentum mesolows—for example, by Adams-Selin and Johnson flux. If the magnitude of the turbulent stress decreases (2010), in which the Oklahoma Mesonet data of about with height (i.e., ›w0y0 /›z . 0), the influence of the tur- s 40–50-km spatial resolution were analyzed. bulence on the momentum balance is a momentum sink To better understand the WTHP phenomenon, espe- in (7). In this situation, wind has to be toward lower cially under strong winds when the uncertainties of both pressure as shown in Fig. 6a. On the other hand, if the the horizontal pressure gradient and turbulent momen- magnitude of the turbulent stress, or the negative tur- tum flux are relatively small, we conduct the following bulent momentum flux, increases with height (i.e., › 0y0 › , analyses: w s/ z 0), the turbulence transport of the momentum contributes to the momentum balance as a momentum 1) We examine the relationship between the observed source in (7), then wind has to be toward higher pressure pressure gradient and the vertical variation of the tur- as shown in Fig. 6b. bulent momentum flux in natural coordinates to in- Evidence of wind toward higher pressure has been vestigate whether the turbulent momentum transport reported in the literature. Prior to sonic anemometers, can explain WTHP using the following two methods: Sheppard et al. (1952) analyzed wind profiles collected First, we directly examine the vertical difference of the from balloon measurements over the northeastern At- observed turbulent fluxes at the two levels around the lantic for a 7-day period and concluded that in a baro- $p measurement level. Second, we apply the bulk clinic PBL, the surface wind is more likely to go toward formula to relate the observed turbulent momentum higher pressure. Evidence for WTHP was also found for flux with wind speed at the two levels and analyze the 3406 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70

FIG. 7. The estimated vertical derivative of the along-wind turbulent momentum ﬂuxes between 5 m (represented by subscript 5) and the lowest sonic-anemometer level (represented by subscript 0) as a function of (a) ›p/›s and (b) S at 5 m for four categories. ‘‘Night’’ and ‘‘day’’ represent the data from local nighttime and daytime. The vertical lines represent the standard deviation of the derivatives in each average bin. Positive ›p/›s corresponds to WTHP. All the data used here are for S . 5ms21.

vertical difference from the fitted relationship between level (0.5 or 1.5 m) (Fig. 7). We focus on the turbulent turbulent momentum fluxes and mean wind speeds. momentum flux for S . 5ms21 as the flux uncertainty The second method depends on the averaged relation- generally increases with decreasing wind speed owing to ship between turbulence and wind speed but avoids the unknown sporadic submeso motions. In addition, strong flux uncertainty in each flux estimate. turbulent mixing associated with strong wind reduces 2) We then investigate the reason behind the observed vertical variations of wind direction to the point that the relationship between ›p/›s and S in Fig. 5c and directional variation of the turbulent flux is negligible. between ›p/›y and y in Fig. 5a based on the fitted However even under strong winds, the submeso fluxes dependence of the turbulent momentum flux on wind can occasionally influence the turbulent flux at higher speed under moderate to strong winds. levels (section 2), which is reflected in the relatively 3) We then explore the possibility of WTHP by using large standard deviation of the vertical momentum flux a simple PBL mixing model. The exercise here is to difference for a relatively small range of wind speed in demonstrate that WTHP can happen at least under Fig. 7b. Under moderate to strong winds, the covariance specified realistic baroclinic conditions and not to spectra at the observation heights are similar to the ones explore sufficient and necessary conditions for WTHP. in Fig. 3; that is, the contribution of large eddies increases with height while the contribution of small eddies de- a. Relationship between the horizontal pressure creases with height. We average the vertical flux differ- gradient and the observed turbulent momentum ence in four categories depending on whether wind is flux toward higher or lower pressure and day or night. Over- To investigate the vertical variation of the momentum all, the magnitude of the downward turbulent momentum flux at the pressure-sensor level, we use the turbulence flux is larger at the upper level than the lower level in all measurements at 5 m and at the lowest sonic-anemometer the categories and the vertical flux difference may be NOVEMBER 2013 S U N E T A L . 3407 slightly larger during daytime than at night perhaps An increase of the turbulent momentum flux with because of the diurnal variation of the atmospheric sta- height has also been observed by Pennell and LeMone bility. On average, the vertical flux difference is larger (1974) and Desjardins et al. (1989) using aircraft data. for WTHP (›p/›s . 0) than for WTLP (›p/›s , 0) be- The possible occurrence of WTHP and the vertical in- cause both the wind speed and the horizontal pressure crease of the turbulent momentum flux are further in- gradient are stronger for WTHP than for WTLP during vestigated later in this section by using a simple PBL CASES-99 (Fig. 7a). balance model. Traditionally, the turbulent flux is assumed constant For the crosswind momentum balance, the relevance of with height in the surface layer. If the increased contri- the curvature term in the crosswind momentum balance bution of large eddies to the turbulent flux with height compared to the Coriolis force is determined by the exactly compensates for the decreased contribution Rossby number defined at the beginning of this section. 2 of small eddies, the turbulent flux would be constant with For a 10 m s 1 wind, the curvature term is negligible for height. The results in Fig. 7 imply that the increase of the R . 10 km. The observed nearly linear relationship be- large-eddy contribution to the turbulent flux is greater tween ›p/›n and S for S . 5ms21 for both southerly and than the decrease of the small-eddy contribution under northerly winds in Fig. 5d suggests that the curvature term, 2 moderate to strong winds, which is also evident in Fig. 3. S /R, is relatively small. For wind speed stronger than 2 Therefore, the observation of the vertical variation of the about 5 m s 1, a significant fraction of the large values of turbulent momentum flux suggests the existence of WTHP ›p/›n are negative (Fig. 5d). Negative ›p/›n is opposite to as long as the airflow is approximately in equilibrium, the Coriolis force in (8). This result implies that the which is independent of the pressure measurement. Coriolis force is relatively important in the crosswind Sun et al. (2012) found that when the wind is below a momentum balance at the CASES-99 site. The crosswind threshold wind value for a given observation height in momentum flux is much smaller than the along-wind flux, a stably stratified atmosphere, turbulence generated at and its vertical variation is not systematic as for the along the ground rapidly decreases with height. However, wind; therefore, we do not examine it here. once wind speed is stronger than the threshold at the b. Relationship between wind speed and the observation height, large turbulent eddies, which scale along-wind horizontal pressure gradient with the layer depth, can be generated by the bulk shear—that is, a strong shear across the entire layer We investigate the relationship between ›p/›s and S in between the observation height and the ground. Simi- Fig. 5c, which is also similar to the relationship between lar results were found by Mahrt et al. (2012) and Van de ›p/›y and y in Fig. 5a. Assuming the along-wind pres- Wiel et al. (2012). As shown in Fig. 3, the large eddies sure gradient balances the vertical convergence of the can effectively contribute to the turbulent flux through along-wind turbulent momentum flux, we can associate their large amplitudes. As the amplitude of large eddies the horizontal pressure gradient with the vertical dif- decreases toward the ground, the contribution of the ference of the turbulent momentum flux expressed in large eddies to the turbulent momentum flux decreases the surface bulk formula. Applying the surface bulk significantly. formula for the along-wind momentum flux at both 5 m Turbulence can also be generated by strong local in- (represented by subscript 5) and the lowest sonic ane- stabilities (either thermal or shear instability) well above mometer level (0.5 or 1.5 m, represented by subscript 0), the ground; for example, below a nocturnal low-level jet the along-wind momentum flux can be expressed as (LLJ) (Banta et al. 2002), turbulence can increase with height (i.e., the so-called upside-down nocturnal bound- 0y0 j 52 2 w s 5 CDS and (9) ary layer). Under this situation, the downward turbulent momentum flux can converge vertically (Banta et al. 0y0 j 52 2 w s 0 CD0S0 , (10) 2006), corresponding to a momentum source. There- fore, the magnitude of the downward turbulent mo- where mentum flux can increase with height not only under a nocturnal LLJ, but also with strong winds when the 5 2 d CD0 CD CD , (11) contribution of large eddies to the turbulent flux is en- 5 2 d hanced. As a result of the increase in magnitude of the S0 S S, (12) turbulent momentum flux with height, the vertical turbulent momentum flux converges toward the surface CD is the drag coefficient at 5 m, and dCD and dS are the and provides a momentum source, which can approxi- departures of CD and S at the lowest sonic anemometer mately balance the strong wind toward higher pressure. level from their 5-m values, respectively. Substituting 3408 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70

(9)–(12) into (7) and assuming the atmosphere is in equilibrium, we have antitriptic balance,

› w0y0 j 2 w0y0 j 1 p ’ 2 s 5 s 0 r ›s dz

1 2 5 [C S 2 (C 2 dC )(S 2 dS)2] dz D D D 2 2 C S dC d 2 C S 5 D 2 2 D 2 S 5 D d 1 1 1 d A, z CD S z (13) where dC dS 2 A [ 1 2 1 2 D 1 2 , (14) CD S and dz is the vertical distance between 5 m and the lowest sonic anemometer level. If both A and CD are invariant at aﬁxedz, the antitriptic balance along the wind direction in (13) implies

›p 2 ; S . (15) ›s

In addition, if A . 0, (13) also implies that the magni- 0y0 tude of negative w s increases with height. We examine A in (14) using the observations at 0.5, 0 0 FIG. 8. (a) The along-wind momentum flux (w y ) as a function 1.5, and 5 m for S . 5ms21. Because dS/S approaches s i of wind speed Si at i = 0.5, 1.5, and 5 m above the ground. The 0y0 2 a constant as S increases no matter whether S0 is at 1.5 or curves are least-square fits of (w s)i as functions of Si at the 0.5 m (Fig. 8b), and CD is approximately invariant under three levels using only observations when wind speed at 5 m . 21 neutral conditions (strong winds) at a given z (Fig. 8a), S 5ms . (b) The wind speed ratios between 5-m S and the lowest sonic anemometer level S as functions of S. The horizontal A is invariant under strong winds. We relate the ob- 0 lines in (b) mark the constant ratios at the strong wind limit at the › › y . 21 y , served p/ s and S for 5ms and for 0 using the two levels. following relationship: › › y . 21 ›p 2 different relationships between p/ s and S for 5ms 5 aS 1 b, (16) y , ›s and 0 may also reflect the influence of atmospheric stability on the relationship. In addition, antitriptic bal- 2 2 where a (hPa s2 m 3)andb (hPa m 1) are fitted con- ance may not be valid under weak winds because non- stants. The coefficient b allows for a small adjustment stationarity under the influence of sporadic submeso because overall, the observed flow seems not exactly in motions can be an issue, and all the momentum terms equilibrium. Figure 5c shows that the observed ›p/›s is may have similar magnitudes. Similarly ›p/›y is well indeed closely related to the wind speed squared for correlated to y2 as shown in Fig. 5a. y . 5ms21 and for y , 0, which suggests that antitriptic Using the fitted relationship between the observed 0y0 . 21 balance is approximately valid in the along-wind di- w s and S at 0.5, 1.5, and 5 m for S 5ms (Fig. 8a), we rection at least for the moderate to strong winds asso- obtain CD at each level. Using both the estimated CD and ciated with the WTHP events. The relatively large dS/S at each level, we find positive A no matter whether systematic deviation of the observed low winds from the the lowest sonic anemometer was at 0.5 or 1.5 m. Positive fitted relationship for y . 5ms21 (green line in Fig. 5c) A suggests that on average the magnitude of the down- suggests that the atmospheric stability, which we ignore in ward turbulent momentum flux increases with height; that the derivation of (15), could be a factor in the relationship is, the turbulent momentum flux transfer is a source term between ›p/›s and S. Since the data for y , 0inFig.5c in the momentum balance, which allows WTHP. There- are dominated by relatively weak winds, the observed fore, the observed relationship between the quadratic wind NOVEMBER 2013 S U N E T A L . 3409 speed and the horizontal pressure gradient further sug- K (z) K~ (z) 5 m (24) gests the existence of WTHP. m u h *0 c. A simple mixing model in barotropic and 5 kz 2 : z 2 2z6 1 ~ baroclinic environments (1 0 9 ) exp( ) Km0 , (25) To theoretically explore the possibility of the sur- ~ face wind blowing toward higher pressure and the where z 5 z/h and Km0 5 0:0002, which is plotted in magnitude of the downward momentum flux in- Fig. 9a. creasing with height, we present here an analysis using We assume a baroclinic environment where both Ug 21 a simple PBL eddy diffusivity model for both baro- and Vg increase linearly with height from Ug 5210 m s 21 tropic and baroclinic conditions in geotriptic balance. and Vg 521ms at z 5 0to›Ug/›z 5 ›Vg/›z 5 0 To be able to specify the vertical variation of the for z . 1. We consider two cases for 0 , z # 1: case 1, 21 horizontal pressure gradient through the geostrophic ›Ug/›z 5 ›Vg/›z 5 0.02 s ,andcase2,›Ug/›z 5 ›Vg/›z 5 2 relationship, we use Earth coordinates. Using the 20.005 s 1. The vertical variation of geostrophic wind in geostrophic relationship, cases 1 and 2 corresponds to equal temperature gradients 2 in x and y direction of about 6 3 10 5 and 21.5 3 › 25 21 52 p 10 Km , respectively. For comparison, we also pres- fcUg and (17) ~ 21 ›y ent a barotropic case with the same Km(z), Ug 5 10 m s , 21 and Vg 5 19 m s , which are the geostrophic wind values ›p 5 5 21 f V 5 at z h for case 1. In addition, we choose u 0 0.5 m s c g › , (18) * x and h 5 103 m for all the cases. The above cases are chosen only to demonstrate different baroclinic situations the geotriptic equations of motion can be written as and a barotropic situation, not to simulate any observed › ›u cases as we do not know the vertical variation of the 2f [y(z) 2 V (z)] 5 K (z) and (19) horizontal pressure gradient nor the geostrophic wind c g ›z m ›z during CASES-99. › ›y The resulting wind for the barotropic case is to- f [u(z) 2 U (z)] 5 K (z) , (20) c g ›z m ›z ward lower pressure and the magnitude of the downward momentum flux decreases with height (Figs. 9b,c,e). For case 1, which represents warm advection where Ug and Vg are geostrophic wind components in x (see below), the surface wind is toward higher pres- and y directions, and Km(z) is the eddy viscosity. In (19) and (20), the momentum fluxes in x and y directions are sure, and the magnitude of the downward momentum flux increases with height up to z ’ 360 m and decreases above it (Figs. 9b–e). Similar to the baro- t (z) ›u x 52K (z) and (21) tropic case, the surface wind in case 2, which repre- r m ›z sents cold advection (see below), is toward lower t pressure and the magnitude of the downward mo- y(z) ›y 52K (z) . (22) mentum flux decreases with height throughout the r m ›z PBL (Figs. 9b,c,e,f). We neglect any dependence of the eddy viscosity on Hoxit (1974) investigated the different baroclinic ef- baroclinity (Arya and Wyngaard 1975), and base our fects of cold and warm advection on ageostrophic winds by extending the work of Sheppard et al. (1952). He Km(z) on the expression given by Collins et al. (2004) for neutral conditions, found that baroclinity increases (decreases) the ageostrophic wind components toward lower pressure in cold z 2 (warm)-air advection. Arya and Wyngaard (1975) also K (z) 5 u kz 1 2 , (23) m *0 h found that the surface cross-isobar angle is a function of the thermal wind, with larger values occurring for where h is the PBL height, k is the von Karm an constant, warm-air advection and smaller values for cold-air and u*0 is the surface friction velocity. We slightly modify advection. Km(z) by an exponential function so that it transits In case 1, the thermal wind is southwesterly; that is, smoothly into the free troposphere at z 5 h and results the air is generally warmer in the southeast sector and in a well-behaved analytical solution for (19) and (20). colder in the northwest sector (Fig. 10a). The thermal Writing it in a dimensionless form, we have wind results in the geostrophic wind turning clockwise. 3410 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70

FIG. 9. (a) The normalized eddy viscosity as a function of the normalized height (z 5 z/h), (b) the hodograph in Earth coordinates, and (c) the wind speed S and (e) the turbulent momentum ﬂux as a function of z for the three cases. (d),(f) The wind vectors at several values of z, horizontal pressure contours (black dashed lines), and temperature contours (magenta dashed lines) for cases 1 and 2 are shown.

As the surface southerly wind approaches the geostrophic produce WTHP. A more thorough analysis is required to wind with height, the resulting south wind in this case demonstrate the necessary and sufficient conditions for blows from the warm to the cold sector throughout the wind toward higher/lower pressure. PBL and toward higher pressure. These results suggest that warm-air advection can lead to WTHP. In contrast, the thermal wind is northeasterly for case 2, 4. Discussion and the air is warmer in the northwest sector and colder a. Duration of wind toward higher pressure in the southeast sector (Fig. 10b). Thus, the thermal wind leads to the geostrophic wind turning counterclockwise. As the CASES-99 observation domain is about 500 m 3 The resulting east-northeast flow in this case blows from 500 m, we can only address the duration of the WTHP the cold to the warm sector throughout the PBL, and the occurrence and not the spatial scale. As expected, the wind is toward lower pressure. number of WTHP events decreases with the event du- These three cases show examples of the equilibrium ration (Fig. 11), where a WTHP event is defined as a momentum balance when wind is toward higher/lower continuous time period when the directional difference pressure. It remains to be determined whether warm between wind and $p remains less than a specified value. advection is a necessary condition for WHTP or whether In Fig. 11, we choose two values, 6458 and 6908,to the dynamic characteristics of strong winds can also evaluate the sensitivity of the number frequency of the NOVEMBER 2013 S U N E T A L . 3411

FIG. 11. (a) The number of WTHP events as a function of the event duration, and (b) the correlation between the event duration and the mean wind speed of the event at 5 m for the two deﬁnitions of WTHP.

FIG. 10. The specified geostrophic wind Vg at z 5 0 and h, the corresponding thermal wind Vt within the PBL, and the wind vector V at z 5 10 m for (a) the warm advection (red vector) and Irene, which were separated by a high-pressure ridge, was (b) the cold advection (blue vector), respectively. The black and large. Shortly after 1500 UTC (1000 LDT), the surface red dashed lines are the pressure and temperature contours, re- pressure started to decrease and the strength of the spectively. southerlies started to increase in the Kansas area. The surface pressure remained relatively low and steady for WTHP event to the event definition. There are a number about 5 h after the large initial decrease. The horizontal of events that last longer than 10 h no matter which def- pressure gradient based on two Automated Surface Ob- inition we use. By relating the averaged wind speed serving System (ASOS) stations (Nadolski 1998) sepa- during each event and the length of each event, we find rated by about 20 km southwest of the CASES-99 site was that the longest WTHP event lasted about 30 h and on the same order of magnitude as the one observed at 2 occurred at a relatively strong wind of 6 m s 1 for the the CASES-99 site. In addition, the National Weather 6458 definition (Fig. 11b). If we relax the definition to Service (NWS) reported a maximum wind gust of about 2 6908, another WTHP event longer than 30 h occurred 15 m s 1 around 2200 UTC over the surrounding central 2 at about 3 m s 1. These results suggest that the WTHP Kansas area of approximately 200 km 3 200 km, which event is not just a random, small-scale phenomenon; it was consistent with the strong wind associated with may occur on the synoptic scale as well. the strong horizontal pressure gradient observed at the The strongest WTHP event, occurring on 15 October, CASES-99 site. Therefore, the strongest WTHP ob- is associated with a strong low pressure system. On this served at the site may be similar to the physical process in day, the synoptic map indicates that Hurricane Irene the mesolows described in Johnson (2001) although no was southeast of Florida, and a low-pressure center severe precipitation was involved. moved slowly southeastward toward the CASES-99 site. Because the magnitude of the turbulent flux has to The surface pressure gradient between the low pressure decrease toward the PBL top, the observed increase in northwest of the site and the low pressure associated with magnitude of the downward along-wind turbulent flux 3412 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70 with height for WTHP has to reverse and decrease with approximately linear relationship between the 30-min- height somewhere higher up within the PBL as dem- averaged crosswind pressure gradient and wind speed for onstrated in the simple PBL balance model in section 3c. either y . 0ory , 0, R must be relatively large dur- This suggests that the PBL during CASES-99 had to be ing CASES-99. Thus, the observations suggest that baroclinic if the PBL was in quasi equilibrium. Thus, the Ro 5 S/(fcR) is relatively small and the Coriolis force is increasing contribution of large eddies to the turbulent important in the crosswind direction during CASES-99. flux observed during CASES-99 could be associated Therefore, the airflow during CASES-99 is approxi- with baroclinity. However, whether the baroclinity is the mately geotriptic. key behind WTHP needs to be further explored. b. Wind toward lower pressure and the weak 5. Summary southerly wind Our unique dataset is of sufficient quality to take a For the observed WTLP cases during CASES-99, both new look at the momentum balance at the bottom of the the wind speed and the horizontal pressure gradient are atmosphere. We find that about 50% of the time during mostly weak. The weak southerly wind is found to be CASES-99, wind is toward higher pressure, which in- dominated by the nighttime cold air moving northward cludes all of the observed winds. If we restrict the obser- from the small gullies south and southwest of the 60-m vations to wind speed at 5 m above the ground stronger 2 tower. When this happens, the temperature at tower 5 than 5 m s 1, wind toward higher pressure occurred in tends to be about 0.58C or more lower than that at tower 2, about 40% of these cases, or about 20% of the entire and the pressure is about 0.02 hPa higher at tower 5 than time. For these moderate to strong wind cases, the hori- at tower 2. Interestingly, the weak southerly wind at night zontal pressure gradient is large, the turbulent flux un- is dominated by WTLP events, which is consistent with certainty is relatively small, and the vertical variation of the cold advection case from the simple PBL balance wind direction is negligible. As demonstrated in Sun et al. model in section 3c. (2012), the bulk shear in strong wind cases can generate During CASES-99, all the WTLP cases have weak large eddies. We find that the contribution of large eddies winds except for a few moderate wind cases. The mag- to the turbulent momentum flux increases with height. nitude of the downward along-wind momentum flux in- Through the vertical turbulent momentum flux transport, creases with height for those cases, similar to WTHP with this provides a mechanism for a momentum source above the same wind conditions. For those cases, the flow ac- the ground instead of a sink or an ‘‘internal friction’’ as celeration cannot be neglected in the momentum balance sometimes described. Because of this momentum source, as both the horizontal pressure gradient and the vertical the surface wind can be toward higher pressure, which turbulent transport are momentum sources. Our obser- acts to decelerate the airflow (Fig. 6b). Based on the re- vation of few strong wind cases with WTLP is another lationship between turbulence and mean wind speed indication of lack of significant flow acceleration during under antitriptic balance in the along-wind direction, the CASES-99. Further investigation is needed. observed approximate relationship between the along- wind pressure gradient and the quadratic wind speed c. Antitriptic and geotriptic balances under strong winds further suggests an approximate The observations in this study demonstrate that the balance between the horizontal pressure gradient and the vertical turbulent momentum transfer, which appears vertical turbulent momentum transfer. The observed in both antitriptic and geotriptic balances, needs to be wind toward lower pressure occurs most often with weak interpreted correctly. It is not sufficient to know just the southerly wind, which is often associated with cold ad- surface momentum flux when considering the momen- vection from the gullies south and southwest of the site. tum balance. The vertical momentum transfer by the Thus, wind toward higher pressure is not only observed turbulent flux does not always act as a drag or ‘‘friction’’ directly through wind and pressure measurements, but it as it is often called; it can be a momentum source in a is also indirectly confirmed through the observed vertical baroclinic environment. Consequently, the surface wind convergence of the turbulent momentum flux and the may be driven by not only the horizontal pressure gra- relationship between wind speed and horizontal pressure dient but also by the vertical convergence of the turbulent gradient. momentum flux. The observed crosswind pressure gradient is approxi- The importance of the Coriolis force in the momentum mately linearly related to the wind speed especially under balance relative to flow acceleration can be easily eval- strong wind, suggesting that the curvature term and the uated in natural coordinates because it only appears Rossby number associated with the radius of the air in the crosswind direction. Based on the observed trajectory are small. The observed negative pressure NOVEMBER 2013 S U N E T A L . 3413 gradient in the crosswind direction further implies the Colle, B. A., and C. F. Mass, 1996: An observational and modeling contribution of the Coriolis force in the crosswind mo- study of the interaction of low-level southwesterly flow with mentum balance. Thus airflow during CASES-99 is ap- the Olympic Mountains during COAST IOP 4. Mon. Wea. Rev., 124, 2152–2175. proximately geotriptic. Collins, W. D., and Coauthors, 2004: Description of the NCAR Using a simple PBL eddy diffusivity model, we find Community Atmosphere Model (CAM 3.0). NCAR Tech. Rep. that warm advection can lead to the magnitude of the NCAR/TN-4641STR, 214 pp. downward turbulent momentum flux increasing with Cuxart, J., G. Morales, E. Terradellas, and C. Yague,€ 2002: Study of height and wind blowing toward higher pressure, while coherent structures and estimation of the pressure transport terms for the nocturnal stable boundary layer. Bound.-Layer cold advection or a barotropic PBL results in the mag- Meteor., 105, 305–328. nitude of the turbulent momentum flux decreasing with Desjardins, R. L., J. I. MacPherson, P. H. Schuepp, and F. Karanja, height and wind blowing toward decreasing pressure. The 1989: An evaluation of aircraft flux measurements of CO2,water role of the baroclinity for WTHP from the model result is vapor and sensible heat. 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